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Overcritical free-surface shapes, isolines of the dimensionless potential (left) and of the dimensionless concentration (right) at the applied field intensity γ = 1.265. Solid (dashed) shape-lines corresponds to the non-uniform (uniform) particle distribution.
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The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak‐shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematical model describes a single peak in the pattern ass...
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Magnetic fluid flow and heat transfer by natural and thermomagnetic convection was studied numerically in a square enclosure. The aim was to investigate the transition from natural convection to thermomagnetic convection by exploring situations where buoyancy and the Kelvin body force would be opposing each other such that the magnetic effects woul...
Citations
... A special challenge is studying materials with nonlinear physical properties [8,11], in particular soft magnetic materials [28]. Computational approaches of handling equilibrium states of ferrofluid systems with different geometries and free surfaces -drop, layer, capillaryhave been developed in [16,17,18,19,23] for uniform applied magnetic fields. ...
A coupled method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics. The problem describes an interaction of a uniform magnetic field with a cylindrical ferrofluid layer. Ferrofluid magnetisations, based on expansions over the Langevin law, are considered to model ferrofluids with a different concentration of ferroparticles. The shielding effectiveness factor of the cylindrical thick-walled ferrofluid layer is calculated depending on intensities of the uniform magnetic field and on thickness of the ferrofluid layer.
... A third explanation is an inhomogeneous distribution of magnetic particles due to magnetophoresis [37] taking place while the field is at B 1 . We consider this less likely because of the enormous time scales of such a process at the large viscosity of the experimental fluid. ...
... Third, magnetophoresis may take place in the crests of the pattern, creating an inhomogeneous distribution of magnetite. Even though the timescale for separation in a low viscosity MF is in days [37,42] and our measurements last only hours, an effect cannot be completely excluded. ...
Using a highly viscous magnetic fluid, the dynamics in the aftermath of the Rosensweig instability can be slowed down by more than 2000 times. In this way we expand the regime where the growth rate is predicted to scale linearly with the bifurcation parameter by six orders of magnitude, while this regime is tiny for standard ferrofluids and cannot be resolved experimentally there. We measure the growth of the pattern by means of a two-dimensional imaging technique, and find that the slopes of the growth and decay rates are not the same - a qualitative discrepancy with respect to the theoretical predictions. We solve this discrepancy by taking into account a viscosity which is assumed to be different for the growth and decay. This may be a consequence of the measured shear thinning of the ferrofluid.
... Cowley et al. were the first who observed this phenomenon experimentally [20]. Later on, Rosensweig instability was investigated analytically and numerically assuming a uniform ferromagnetic particle distribution in the bulk of the magnetic fluid for any applied field intensity [23]. This unique property of ferrofluids to change shape and retain properties of a liquid when a magnetic field is applied, allows them to be utilized in a wide range of technological applications. ...
In this work, we present experimental observations on the colloidal phase transitions (from liquid phase to solid phase) involving evaporation at different time scales. Two experimental setups have been used: vertical deposition configuration (large duration and low evaporation) and spin- coating (short duration and high evaporation) to carry out various research objectives.
(a) We study patterns formation in vertical deposition of colloids on applying weak AC fields at various temperatures. Diluted suspension of negatively charged polystyrene particles of 1.3 μm in diameter suspended in ultra pure water are used to perform several experiments at different evaporation in external weak AC fields (0.8 V/mm to 1.2 V/mm and of frequency from 1 Hz to 3 Hz). At room temperature the application of AC field leads to the formation of one dimensional clusters array at the interface. The dynamical flows of the system during clusters formation in external AC fields have been studied by PIV analysis. Also, we demonstrate the effect of increasing initial particle concentration (0.5% to 1.1% (w/w)) on the clusters evolution. At higher temperature (63 ◦ C) we obtain ordered columnar deposits of these colloidal suspensions in AC fields. We study the effect of field strengths on the behavior of columns formation. (b) We obtain polycrystals of mono-layer on photo-patterned substrates by spin-coating using concentrated colloidal suspension of 458 nm diameter silica spheres dispersed in ethanol 95% of 20% (V/V) concentration. We break the axial symmetry imposed by spin axis and eliminate the emerging OCP character (6– or 4–arms). The effect of scaling spacing of surface patterning on the different structures formation of the spin-coated deposits has been studied extensively. We analyze the different structures in depth with bond order parameters and with Minkowski structure metrics. Also, we investigate the influence of external magnetic fields on the flow dynamics of mixed colloidal particles suspension (carbonyl iron and silica particles of micrometer size) by spin-coating and to manipulate the magneto-rheology in terms of occupation factor of the resulting deposits. We develop a generalized model by modifying Cregan and O’Brien model [1] to measure the change in relative viscosity of the mixed colloids in magnetic fields.
[1] V. Cregan, S. O’Brien. A note on spin-coating with small evaporation. J. Colloid Interf. Sci. 314, (2007), p. 24.
... The most theoretical models for the diffusion process in magnetic fluids assume no interaction between particles (Bashtovoi et al., 2007;Lavrova et al., 2010;Polevikov & Tobiska, 2008;, which is valid for dilute fluids only. This assumption allows to construct an explicit dependence between equilibrium particle concentration and the magnetic field distribution, simplifying significantly the modelling. ...
... A number of papers are devoted to numerical investigations of the Rosensweig instability. The numerical results concern equilibrium states of the ferrofluid layer in (Aristidopoulou et al., 1996;Bashtovoi et al., 2002;Boudouvis et al., 1987;Gollwitzer et al., 2007;2009;Lavrova et al., 2003;2010) and analyze dynamical properties of the ferrofluid behavior in (Knieling et al., 2007;Matthies & Tobiska, 2005). A non-uniform equilibrium distribution of particles in the ferrofluid layer is computed in (Lavrova et al., 2010) for the first time. ...
... The numerical results concern equilibrium states of the ferrofluid layer in (Aristidopoulou et al., 1996;Bashtovoi et al., 2002;Boudouvis et al., 1987;Gollwitzer et al., 2007;2009;Lavrova et al., 2003;2010) and analyze dynamical properties of the ferrofluid behavior in (Knieling et al., 2007;Matthies & Tobiska, 2005). A non-uniform equilibrium distribution of particles in the ferrofluid layer is computed in (Lavrova et al., 2010) for the first time. ...
For the stability analysis or dynamic analysis of the interface phenomena of magnetic fluids as the Rosensweig instability, this paper presents mainly a magnetic analysis with reduced loads, since magnetic fields must be re-calculated every time step the interface changes. This method adopts the indirect boundary element method (IBEM), since the behavior of the surface can be explained mainly by the magnetic stress difference obtained from the interface magnetic field. Starting with Green’s theorem applied for harmonic fields, the magnetic potential and the normal magnetic induction are obtained separately through the density of singular sources on boundaries. The problems of sharp-pointed peaks on the interface, or edges and corners where boundaries cross are avoided easily. The magnetic field, the interface stresses and the fluid velocity are calculated on the largely-deformed interface in a two-layered system of fluid and vacuum domain under a homogeneous vertical magnetic field. In consideration of the nonlinear equation of motion of the pattern amplitude (C.Gollwitzer et al., 2010), the sum of interface stresses and the normal fluid velocity are shown in the phase space of the height of the solitary-wave interface profile and the intensity of the applied magnetic induction. This IBEM is compared with another method called Magnetic Analysis for General Use (MAGU, Y.Mizuta, 2011) on the formulation basis, and their extension to the nonlinear magnetization is discussed.
The present study is devoted to the development of an ADI approach to simulate two-dimensional time-dependent diffusion process of ferromagnetic particles in magnetic fluids. Specific features of the problem are the Neumann boundary conditions. We construct an ADI scheme of formally second order accuracy approximation in time and space. It is proved that the scheme is absolutely stable and it has the accuracy in the energy norm of the second order in time and the order /2 in space. The numerical results of a test problem indicate that the convergence rate in space is of the second order as well.
